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Volume 35, Issue 3
Stochastic Averaging Principle for Mixed Stochastic Differential Equations

Yuanyuan Jing, Yarong Peng & Zhi Li

DOI: 10.4208/jpde.v35.n3.3

J. Part. Diff. Eq., 35 (2022), pp. 223-239.

Published online: 2022-06

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  • Abstract

In this paper, an averaging principle for the solutions to mixed stochastic differential equation involving standard Brownian motion, a fractional Brownian motion $B^{H}$ with the Hurst parameter $H>\frac{1}{2}$ and a discontinuous drift was estimated. Under some proper assumptions, we proved that the solutions of the simplified systems can be approximated to that of the original systems in the sense of mean square by the method of the pathwise approach and the Itô stochastic calculus.

  • Keywords

Averaging principle, mixed stochastic differential equation, discontinuous drift, fractional Brownian motion.

  • AMS Subject Headings

26A42, 26A33, 60H05

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

jingyy120920@163.com (Yuanyuan Jing)

15303412095@163.com (Yarong Peng)

lizhi_csu@126.com (Zhi Li)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-35-223, author = {Jing , YuanyuanPeng , Yarong and Li , Zhi}, title = {Stochastic Averaging Principle for Mixed Stochastic Differential Equations}, journal = {Journal of Partial Differential Equations}, year = {2022}, volume = {35}, number = {3}, pages = {223--239}, abstract = {

In this paper, an averaging principle for the solutions to mixed stochastic differential equation involving standard Brownian motion, a fractional Brownian motion $B^{H}$ with the Hurst parameter $H>\frac{1}{2}$ and a discontinuous drift was estimated. Under some proper assumptions, we proved that the solutions of the simplified systems can be approximated to that of the original systems in the sense of mean square by the method of the pathwise approach and the Itô stochastic calculus.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v35.n3.3}, url = {http://global-sci.org/intro/article_detail/jpde/20773.html} }
TY - JOUR T1 - Stochastic Averaging Principle for Mixed Stochastic Differential Equations AU - Jing , Yuanyuan AU - Peng , Yarong AU - Li , Zhi JO - Journal of Partial Differential Equations VL - 3 SP - 223 EP - 239 PY - 2022 DA - 2022/06 SN - 35 DO - http://doi.org/10.4208/jpde.v35.n3.3 UR - https://global-sci.org/intro/article_detail/jpde/20773.html KW - Averaging principle, mixed stochastic differential equation, discontinuous drift, fractional Brownian motion. AB -

In this paper, an averaging principle for the solutions to mixed stochastic differential equation involving standard Brownian motion, a fractional Brownian motion $B^{H}$ with the Hurst parameter $H>\frac{1}{2}$ and a discontinuous drift was estimated. Under some proper assumptions, we proved that the solutions of the simplified systems can be approximated to that of the original systems in the sense of mean square by the method of the pathwise approach and the Itô stochastic calculus.

Jing , YuanyuanPeng , Yarong and Li , Zhi. (2022). Stochastic Averaging Principle for Mixed Stochastic Differential Equations. Journal of Partial Differential Equations. 35 (3). 223-239. doi:10.4208/jpde.v35.n3.3
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